2. According to a survey, 75% of all customers will return...

2. According to a survey, 75% of all customers will return to the same grocery store. Suppose six customers are selected at random. a) How many customers would be expected to return to the same store? b) Let X be the number of returning customers. Create a probability distribution for X. c) Graph the probability distribution for X using a histogram. d) What is the probability that ? i. no more than 2 customers will return . ii. at least 4 customers will return .

Transcript

00:01 In this question, the x variable shows here number of customers and p shows probability of customers.

00:21 And therefore, x belongs to binomial expression, that is n comma p, which is equal to the n value is equal to 8 and p value is equal to 0 .68.

00:36 So here by using the binomial expression probability of x is equal to x is equal to so 8 x ways and 0 .63 here is the value is 0 .63 whole power x and 0 .37 whole power 8 minus x.

01:05 So here is the x value 0 comma 1 comma 2 comma and so on up to x.

01:11 This is the expression so we have used in this problem so let come to the first question so in first question we have to find out the probability for to get exactly so five return so that which is equal to probability of x is equal to five so by using the binomial expression eight five ways and 0 .63 whole power five and here 0 .37 whole power 8 minus 5 so which is equal to value that is 0 .281 so 5 double 1.

01:52 This is the the first probability value so let come to the b question in b1 we have to find out the probability for probability of to all gate 8 so that here 8 8 8 8 8 8 and 0 .63 whole over 8 and 0 .6 3 whole over 8 and 0 .6 37 whole power 8 minus 8 so which is equal to the value is 0 .024816 this is the probability value for second question so similarly let come to the third question that means the c question so in c1 so we had to find out the probability for at least to get six customer returns so can write this one as probability of x greater than are equal to 6 which is equal to summation x is equal to 6 to 8 and probability of x is equal to x so which is equal to summation x is equal to 6 up to 8 8 x ways and 0 .63 whole power x and 0 .37 whole power 8 minus x and now by applying the binomial distribution expression here, 86 ways and 0 .63 whole power 6 ,0 .37 whole power 8 minus 6.

03:31 Place here so 8 6 ways and 0...

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